Teaching Students to Compose & Decompose Geometric Shapes

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  • 0:04 Real-World Geometry
  • 1:11 Vocabulary
  • 1:52 Understanding…
  • 3:11 Area of Decomposed Shapes
  • 4:21 Volume Using Cubes
  • 6:32 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Lowery

Jennifer has taught elementary levels K-3 and has master's degrees in elementary education and curriculum/instruction and educational leadership.

Learning how to compose and decompose shapes can help students to understand more advanced geometric concepts. This lesson will help you teach students how to compose and decompose various shapes in order to determine perimeter, area, and volume.

Real-World Geometry

Students may not realize it, but they are constantly exposed to geometric concepts in the real world. Tiles on a floor, the volume of a cylindrical container, and the distance around the playground all illustrate geometric concepts. Because students come in contact with everyday examples of geometry, it is helpful to use these examples to assist students in thinking about different ways to approach mathematical calculations. Let's follow the steps fifth grade teacher Ms. Paul takes to teach students how to use shape composition and decomposition to further understand perimeter, area, and volume.

Ms. Paul knows that her students have learned about different two- and three-dimensional shapes in previous grade levels. However, it will be important to quickly remind students of plane figures such as triangles, parallelograms, and squares, as well as the solid figure cube (which will be used to calculate volume). To get students up and moving, she has students identify these shapes in objects around the classroom.


After she reviews familiar concepts of geometry with her students, Ms. Paul will discuss lesson-specific vocabulary for students:

  • Perimeter is the distance around the edge of a plane or two-dimensional figure. Perimeter is measured in units.
  • Area is the size of a two-dimensional surface, so it is a measure of the interior space of a shape. Area is measured in square units.
  • Volume is used to measure the interior space of a solid figure. Volume is measured in cubic units.
  • To compose is to build, or put together.
  • To decompose is to break apart.

Understanding Perimeter with Shapes

Ms. Paul first has her students practice visualizing the concept of composing and decomposing shapes. She then has students cut two identical 5-inch squares using construction paper and rulers. She tells students to experiment with putting the shapes together so that they can create a rectangle. In creating the rectangle, they have composed a shape using two smaller shapes. Then she asks students to break apart the rectangle. Now they have decomposed the bigger shape.

Once students have a firm understanding of composing and decomposing shapes, Ms. Paul has them use the same squares to practice determining perimeter. She asks students to write the measurement of 5 inches on each side of both squares. She asks students to determine the perimeter of each square individually, when the rectangle is decomposed. The perimeter of each square is 20 inches. Then she asks students to compose a rectangle like they did previously in the lesson. The rectangle is the same height, but twice as long as each square. Now she asks them to calculate the perimeter of the composed rectangle, and compare that to the perimeter of each square. The perimeter of the composed rectangle is 30 inches.

area perimeter

Area of Decomposed Shapes

Ms. Paul can next have students use one of the squares to calculate area. If the length of each square is 5 inches, the area inside of the square can be determined by multiplying two sides together. Ms. Paul guides students to the conclusion that the area of the square is 25 square inches. For reinforcement of this concept, students should use their rulers to draw square inches within the shape to represent each square unit.


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